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The points A(−3, 1), B(2, 2), C(4, 6) and D(−1, 5), taken in order, form which quadrilateral?

Class 10Coordinate GeometryGeometry — Coordinates
  • AA rhombus
  • BA rectangle
  • CA square
  • DA parallelogram, but neither a rectangle nor a rhombus

Step-by-Step Solution

AB = , BC = , CD = , DA = . Opposite sides are equal in pairs → parallelogram. It is not a rhombus, because adjacent sides and differ; and not a rectangle, because the diagonals AC = and BD = are unequal. A square would need both conditions.
Answer: D) A parallelogram, but neither a rectangle nor a rhombus

Key idea: Distance formula

**Distance** between two points P₁, ₁) and Q₂, ₂):

**PQ = **

This is just the Pythagoras theorem applied to the right triangle formed with horizontal and vertical legs.

**Example**: Distance between (3, 4) and (7, 1).
= .

**Special distance from origin**: distance of from (0, 0) is .

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